In rest of this section, we come to a detailed discussion of the model results for the \(\gamma p\rightarrow K^+\Lambda (1690)\)  reaction obtained by including the \(N(2570)5/2^-\)  resonance. In Table REF  we list the fitted values of the corresponding model parameters. For resonance couplings, we list the reduced helicity amplitudes \(\sqrt{\beta _{\Lambda ^\ast K}}A_j\)  instead of showing their strong and electromagnetic coupling constants separately [1]}, [2]}, [3]}, [4]}, [5]}, since in tree-level calculations as performed in the present work, only the products of the resonance strongnic and electromagnetic coupling constants are relevant to the reaction amplitudes. Here \(\beta _{\Lambda ^\ast K}\)  is the branching ratio for resonance decay to \(\Lambda (1690) K\) , and \(A_j\)  is the helicity amplitude with spin \(j\)  (\(j=1/2,3/2\) ) for resonance radiative decay to \(\gamma p\) . The values in the brackets below the mass \(M_R\)  and width \(\Gamma _R\)  of the resonance \(N(2570){5/2}^-\)  are the corresponding values listed in RPP [6]}, which are quoted from the results of BESIII [7]}. One can see that both the fitted mass and width for the resonance \(N(2570)5/2^-\)  are close to the ranges given by BESIII [7]}.
